Question

Problem Set 2 EC3022 - Industrial Organisation This problem set does not count towards your final grade, but you should still prepare a detailed solution before the tutorial. We will go over the solution in your next tutorial. Question 1 Suppose that Microsoft has acquired Activision Blizzard and decides to sell the game Call of Duty only to the users of its own game console, the Xbox. The inverse market demand for this game among Xbox users is given by \( p(q)=36-q \). Microsoft has the following cost function \( C(q)=24+q^{2} \). Microsoft behaves as a monopolist in this market and charges a uniform price for the game to all Xbox users. 1. What quantity of games, \( q_{1}^{M} \) would Microsoft produce? 2. What price \( p_{1}^{M} \) would it charge for each unit sold? 3. What is Microsoft's profit, \( \pi_{1}^{M} \) ? 4. What is the consumer surplus \( C S_{1} \) ? 5. What is the total market surplus \( T S_{1} \) ? (Note: fized cost should not be taken into account when calculating producer surplus, so producer surplus \( = \) profits + fized costs (i.e. you need to add back fixed costs)) Question 2 Suppose now that the regulator faces uncertainty about the cost of the firm. With probability \( \frac{1}{2} \), the cost is \( C(q)=40 q \) but with probability \( \frac{1}{2} \), the cost is \( C(q)=60 q \). That is, on average, the regulator believes that the cost is \( C(q)=50 q \). 1. Suppose that the firm's cost turns out to be \( C(q)=40 q \). What is the firm's optimal choice of price and quantity if the regulator imposes a cap of \( \bar{p}=50 \) on the price-per-unit? What is the consumer surplus in this case? Hint: with this price cap, the firm's best option is to set a uniform price as in the normal monopoly problem, but that uniform price could be above or below the per-unit price cap. If it is above, the firm is limited to charging the price cap. 1

          Problem Set 2
EC3022 - Industrial Organisation

This problem set does not count towards your final grade, but you should still prepare a detailed solution before the tutorial. We will go over the solution in your next tutorial.

Question 1

Suppose that Microsoft has acquired Activision Blizzard and decides to sell the game Call of Duty only to the users of its own game console, the Xbox. The inverse market demand for this game among Xbox users is given by \( p(q)=36-q \). Microsoft has the following cost function \( C(q)=24+q^{2} \). Microsoft behaves as a monopolist in this market and charges a uniform price for the game to all Xbox users.
1. What quantity of games, \( q_{1}^{M} \) would Microsoft produce?
2. What price \( p_{1}^{M} \) would it charge for each unit sold?
3. What is Microsoft's profit, \( \pi_{1}^{M} \) ?
4. What is the consumer surplus \( C S_{1} \) ?
5. What is the total market surplus \( T S_{1} \) ? (Note: fized cost should not be taken into account when calculating producer surplus, so producer surplus \( = \) profits + fized costs (i.e. you need to add back fixed costs))

Question 2

Suppose now that the regulator faces uncertainty about the cost of the firm. With probability \( \frac{1}{2} \), the cost is \( C(q)=40 q \) but with probability \( \frac{1}{2} \), the cost is \( C(q)=60 q \). That is, on average, the regulator believes that the cost is \( C(q)=50 q \).
1. Suppose that the firm's cost turns out to be \( C(q)=40 q \). What is the firm's optimal choice of price and quantity if the regulator imposes a cap of \( \bar{p}=50 \) on the price-per-unit? What is the consumer surplus in this case? Hint: with this price cap, the firm's best option is to set a uniform price as in the normal monopoly problem, but that uniform price could be above or below the per-unit price cap. If it is above, the firm is limited to charging the price cap.
1

Problem Set 2
EC3022 - Industrial Organisation

This problem set does not count towards your final grade, but you should still prepare a detailed solution before the tutorial. We will go over the solution in your next tutorial.

Question 1

Suppose that Microsoft has acquired Activision Blizzard and decides to sell the game Call of Duty only to the users of its own game console, the Xbox. The inverse market demand for this game among Xbox users is given by p(q)=36-q. Microsoft has the following cost function C(q)=24+q^2. Microsoft behaves as a monopolist in this market and charges a uniform price for the game to all Xbox users.
1. What quantity of games, q1^M would Microsoft produce?
2. What price p1^M would it charge for each unit sold?
3. What is Microsoft's profit, π1^M ?
4. What is the consumer surplus C S1 ?
5. What is the total market surplus T S1 ? (Note: fized cost should not be taken into account when calculating producer surplus, so producer surplus = profits + fized costs (i.e. you need to add back fixed costs))

Question 2

Suppose now that the regulator faces uncertainty about the cost of the firm. With probability (1)/(2), the cost is C(q)=40 q but with probability (1)/(2), the cost is C(q)=60 q. That is, on average, the regulator believes that the cost is C(q)=50 q.
1. Suppose that the firm's cost turns out to be C(q)=40 q. What is the firm's optimal choice of price and quantity if the regulator imposes a cap of p̅=50 on the price-per-unit? What is the consumer surplus in this case? Hint: with this price cap, the firm's best option is to set a uniform price as in the normal monopoly problem, but that uniform price could be above or below the per-unit price cap. If it is above, the firm is limited to charging the price cap.
1

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